I mean that I want to find lambda(1,nvars)to make the function has the minimized value. I just want to set the number of nonzero elements in vector lambda(1,nvars). As normal, I can get the lambda(1,nvars) using CVX. But I can’t know exact number of nonzero elements in vector lambda. Can we fix the the number of nonzero elements in vector variable lambda?

This is not a convex constraint and therefore outside of the scope of CVX. If lambda is integer valued, then (it’s still not convex but) you could treat it as a mixed integer disciplined convex program. However, based on your question it doesn’t sound like this is the case.

I mean that I want to find lambda(1,nvars)to make the function has the minimized value. I just want to set the number of nonzero elements in vector lambda(1,nvars). As normal, I can get the lambda(1,nvars) using CVX. But I can’t know exact number of nonzero elements in vector lambda.

As Bien correctly states, this is a nonconvex formulation. However, it can be expressed using CVX’s mixed-integer capabilities, assuming you have a CVX Professional license and Gurobi or MOSEK installed:

Technically speaking, this does not constrain the number of non-zero values to be exactly 5; it constrains it to be 5 or fewer. But this is the closest you can get.

Keep in mind that cardinality constraints such as these are combinatorial in nature. While mixed-integer solvers will probably have no difficulty reaching a solution for small values of nvars, the complexity grows exponentially as nvars grows.